Shader receive light cast shadow with its color
Enable Refractive Caustic + Glass shader

It's not shadow, it's light!

The effect you see in the picture is a phyisical effect called "caustics".

White light get into the dice volume. There's in a certain quantity of light that is absorbed by the dice's material. Th red component is not absorbed, so is free to get out of the volumes and reach into the camera, letting we see the cube red (different shades of red because not all the cube surroundings are full white light sources). Not all the "filtered" rays (made of red light only) go directly to the camera, some of them also reflected on the plane surface coloring it a bit.

Blender Cycles can emulate that effect if you enable the Caustics by ticking the check boxes near the cursor in the picture below:



First of all you must use a Glass shader, or the light will not penetrate your object's surface.

Without Caustics, the object project a soft shadow on the opposite side of the light source. The plane is grey, so the shadow will result in a darker grey because less light can reach that points.

Refractive Caustics option takes in account the light that travels through a material.



In addition, the base plane from the photo is sligthtly glossy (you can almost see the dice mirrored) so I would suggest to use a mix of a diffuse and glossy shader in order to get some color bleeding also on the sides where the caustics aren't.

Final result: